EP2556489B1 - Alignment of positron emission tomographs using a virtual tomograph - Google Patents

Abstract

Positron emission tomography, possibly in combination with computed tomography, allows in addition to medical diagnostic imaging the quantitative determination of various parameters. Quantitative measurements using tomographs exhibit a severe and unavoidable dependency on the imaging properties of the respective tomograph, which makes quantitative assessment of the results difficult. This relates particularly to multicentric medical studies, which obligatorily require quantitative comparability of the data measured by the participating centers. The methods claimed herein include the definition of a virtual tomograph with defined imaging properties. The claimed methods also cover determination of the imaging properties of different tomographs on the basis of suitable reference measurements and possibly by using a calibration phantom. Based on the definition of the virtual tomograph and the determination of the imaging properties of different tomographs, the methods according to the invention then allow conversion and subsequently standardized and quantitatively comparable representation of the image data recorded by the different tomographs or systems as if all measurements were acquired equally by the virtual system. The method according to the invention therefore supports the quantitative evaluation of image data in multicentric studies.

Description

The positron emission tomography (PET), optionally in combination with computerized tomography (PET / CT), in addition to the medical diagnostic imaging in principle allows the quantitative determination of various parameters. Prerequisites for such quantitative measurements on the patient are the strict observance of standardized examination protocols as well as a calibration or comparison of the tomographs used.
Particularly in the context of multi-centric medical studies, the requirements for uniform examination protocols, the comparison of the tomographs and the methods for the determination of quantitative values are currently being discussed intensively [WAHL09], [BOEL09], [BOEL09b], [DELB06], [SHYA08], [SCHE09].

However, quantitative measurements using tomographs show a strong and unavoidable dependence on the imaging properties of the respective tomograph, in particular the point spread function (PSF), which differs from tomograph to tomograph. Even with otherwise calibrated tomographs or calibrated other medical imaging devices, a quantitative assessment is made difficult due to the different transfer functions. This concerns in particular multi-centric medical studies, which compulsorily require a quantitative comparability of the data measured by the participating centers.

The most commonly used quantitative measure of the activity measured in a tissue in the context of positron emission tomography is the "standardized uptake value" (SUV) in different variants [BOEL09]. It has been shown that the determination of an SUV can be carried out with great repeatability if a strictly defined examination protocol is followed and the same tomograph is used.
However, it is precisely these measurements that may differ greatly if different tomographs are used, even if the devices are calibrated. The cause is above all the partial volume effect (PVE), which causes the activity of smaller objects to be systematically underestimated. This effect is closely related to the spatial transfer function of the respective tomograph. In addition to the spatial resolution determined by the half-width of the transfer function, the exact form of the transfer function also plays a role here.

Different tomographs can thus show very different partial volume effects (PVE) even with the same spatial resolution.

Different methods have been proposed to minimize the influence of PVE on quantitative measurements, in particular SUV measurements [KEYE95] [STRA91] [BOEL03] [WEST06] [SORE07].

In the article Oliver Rousset et al .: "Partial Volume Correction Strategies in PET", PET Clin 2 (2007), 235-249 (Elsevier Saunders ), various methods for partial volume correction are summarized with reference to a large state of the art. The presented techniques include postreconstruction and reconstruction based PVE correction. The article discloses the described prior art with regard to the handling of the PVE in the sense of a correction of the measurement, wherein the illustrated methods have very different properties and can lead to different results. The illustrated measuring methods essentially result in an improvement of the results. Among other things, an iterative deployment of the measured activity distribution by means of a scanner-specific point mapping function (PSF) is disclosed. It is further described that deconvolution-based methods using PSF can not or only to a very limited extent be used, since the resulting noise makes the results unsuitable.

Using these often complex methods, possibly using independent measurements to determine the volume of an object, although it is possible to increase the accuracy of the measurements or extend the available measuring range to smaller objects out, but the results remain dependent on the particular tomograph used.

The usefulness of these methods in the context of multi-centric studies thus remains very limited.

In the context of quantitative PET studies, especially those that need to be done multiple times over a longer period of time or at different locations, a standardized tomograph would be needed, which could provide reproducible measurements anytime, anywhere.

Such a standardized PET system is unfortunately not available, on the one hand as a result of the large number of available different systems from different manufacturers on the other hand due to the constant technical development of the systems and the consequent permanent change of equipment.

Object of the invention and solution

The essential aspect of quantitative measurements is the ability to compare measurements. In the context of PET, a measurement of the SUV can be made as the basis of a therapy control (comparison of several measurements over time), as a basis of a classification (comparison of measurements on several patients) or as part of a medical study (follow-up or classification in a Variety of patients from different groups) as a criterion eg for the effectiveness of a drug.

Much more important than exact absolute quantification in the application is thus the repeatability and in particular the comparability of the measurements, even if different tomographs are used.

This basic requirement de facto means a standardization of the tomographs, in particular a uniform spatial transfer function for all tomographs.
Such a standard tomograph is not available in reality for obvious reasons.

The starting point of the invention is now the development of a method which, starting from an accurate metrological characterization of a particular scanner on the basis of a determination of the respective transfer function, allows to convert the data recorded by a tomograph as if they were from another scanner with a known transfer function been recorded.

In certain circumstances, this allows the definition of a virtual tomograph in such a way that it is possible to convert the image data records taken by different real tomographs in each case as if they had been recorded by the defined virtual tomograph. After this conversion, all data sets recorded by the different real tomographs are directly quantitatively comparable.

The methods claimed here include the definition of a standardized virtual tomograph or a standardized virtual imaging system with a known and defined transfer function as the basis for the comparison of different positron emission tomographs or other medical imaging systems. The claimed methods further include determining the imaging properties of different tomographs or imaging systems based on suitable reference measurements and optionally using a calibration phantom. In addition to particularly favorable technical versions of such a calibration phantom, the claims also describe boundary conditions which should be observed in the measurements, in particular with regard to the linearity of the respective measurements.
Starting from the definition of the standardized virtual tomograph as well as the determination of the imaging properties of different real tomographs, the methods according to the invention then permit a conversion and subsequently uniform and quantitatively comparable representation of the image data taken by the different tomographs or systems as if all the measurements were equal standardized virtual system takes place.

wobei img für das vom jeweiligen Tomographen mit der Transferfunktion psf gemessene Bild steht und F ^-1(H) für die definierte Transferfunktion des standardisierten virtuellen Tomographen. Letztere wird hier als Fouriertransformierte einer Aposidationsfunktion H dargestellt.
Das Ergebnis ist jeweils ein standardisiertes Bild img_n das als Ausgangspunkt für normierte bzw. vergleichbare quantitative Bestimmungen dienen kann.The claimed method for handling a virtual tomograph provides, inter alia, the use of multiple mathematical numerical Operations, in particular a combination of convolution and deconvolution, which is hereinafter referred to as transconvolution .
In the context of the claimed method, the standardized virtual tomograph or a virtual imaging system is first defined by specifying a suitable spatial transfer function and the real tomography or imaging systems are characterized by suitable measurement of the respective spatial transfer function (point spread function, psf ) ,
The numerical process referred to as transconvolution can be represented as a convolution of the respectively measured images with the inverse of the transfer function of the respective receiving tomograph (deconvolution) followed by a convolution of the result with the defined transfer function of the virtual tomograph (convolution). This process can be represented as follows $$\mathit{img}\otimes {\mathit{psf}}^{-1}\otimes F^{-1}\left(H\right)={\mathit{img}}_n.$$

where img stands for the image measured by the respective tomograph with the transfer function psf and F ^-1 ( H ) for the defined transfer function of the standardized virtual tomograph. The latter is represented here as a Fourier transform of an aposidation function H.
The result is a standardized image img _n which can serve as a starting point for normalized or comparable quantitative determinations.

By defining the virtual tomograph or a virtual imaging system as standard, the method according to the invention can thus effectively support the quantitative evaluation of image data in multi-centric studies.

Reference measurements using a dedicated solid state phantom are proposed for determining the respective transfer functions of the different tomographs.
For the handling of the claimed method in the context of medical imaging systems, in particular postal IRON emission tomographs, the reconstruction and joint administration of two different image data sets is proposed with an unchanged acquisition process. One data set is reconstructed for optimum visualization of the images, and a second data set is reconstructed as linearly as possible for the quantitative measurements. This second data set can then be converted on the basis of the known spatial transfer function of the respective tomograph with the aid of a numeric transconvolution, as if the recording had taken place by the standardized virtual system. Quantitative measurements starting from the standardized in this form data set are then normalized and comparable with corresponding other normalized measurements.

The main purpose of the methods is to improve the informative value of clinical trials, and in particular to support and improve multi-center clinical trials.

In addition to an application in the field of post-ion emission tomography, the method can also be used in other complex imaging techniques, such as other tomography, ultrasound imaging or scanning methods such as confocal microscopy.

Relevant aspects of imaging and image editing

Based on the physical properties of light, in particular the propagation of light in the form of an electromagnetic wave, numerical methods in Fourier space and their application in imaging are very well understood. The resulting methods such as Viennese deconvolution or iterative deconvolution based on statistical criteria are established in various fields of imaging or spectroscopy.
The importance of stationary or non-stationary spatial transfer functions (PSF) and physical limits of resolution or image quality due to stationary or non-stationary photon noise is well defined. [ERSO07], [GOOD96].
Accordingly, the effects of discrete sampling in spatial, spectral, or temporal coordinates and the digital representation of intensities are represented in the mathematical models [BENE01]. And the power of today's computers allows the routine use of numerical methods in Fourier space even for large volume data sets, especially in the field of medical imaging.

Nevertheless, it must be explicitly stated that these numerical methods, which were originally developed in the field of Fourier optics, are based directly on the basic physical properties of light in the context of imaging optical devices. A great role is played here by the strictly linear superposition in the limits set by a Poisson statistic of photon noise.

For non-optical medical imaging devices, and especially for tomography, these basic features are not necessarily met primarily. The application of Fourier methods in medical imaging may therefore not exaggerate linear effects and thus complicate a quantitative assessment.

Basics of PET and PET / CT imaging

PET / CT imaging is performed in three distinct steps for both the PET and CT sections: data acquisition, sinogram calculation, and image reconstruction. Each step has its own special properties and parameters and contributes to the performance of the overall system. In addition, the CT is crucial for the attenuation correction of the PET measurements and thus goes directly into the quantification in addition to the PET itself. The technical details of current clinical devices are widely discussed [TARA03] [CHER06] [TOWN08].
The following sections focus on the linearity of these steps as a basis for quantitative measurements.

PET data acquisition

Clinical PET / CT systems continue to benefit from the advancing technological development. Better and faster scintillators, photodetectors, electronics, and computers allowed the transition from 2D acquisition of coincidence signals to full 3D acquisition and now on to "time-of-flight" (TOF) acquisition. Nevertheless, the fundamental principle of coincidence measurement has not changed, and within the limits set by photon noise and background noise, the measurement process remains linear. Although some parameters of the measurement process vary across the field of view or measurement volume, the exact characteristics of the data acquisition as a whole are very well defined based on a fixed arrangement and stable parameters of the scintillators and detectors. Therefore, based on the measurement principle, it can be assumed that PET data acquisition is linear within wide limits.

Calculation of the PET sinogram

Each coincidence event registered during data acquisition is interpreted as an intensity distribution along a "line of response" (LOR) or a "tube of response" (TOR) connecting the scintillators involved.
Each LOR or TOR can be numerically represented by an angle and offset from the center of the field of view. Starting from values for angle and offset as coordinates, the sinogram is then generated by numerical projection of the coincidence events into a 2- or 3-dimensional coordinate system ie a corresponding data volume.
The process can be used concurrently to make an attenuation correction by increasing the relative weighting of LORs according to a previously calculated attenuation mask to compensate for the attenuation. Furthermore, certain corrections can be incorporated via the TOR concept by numerically varying the diameter of the TOR in order, for example, to include peculiarities of the geometric arrangement of the detectors or different detection sensitivities [HERR07]. Similarly, time of flight information (TOF) can be included to limit the relative contribution of an event to only a subset along the LOR or TOR.
In any case, during or after the projection, interpolation and resampling must occur so that the resulting data set can be provided in a form suitable for the following numerical methods, regardless of the exact geometric arrangement of the detectors. A suitable and frequently used method is the "Fourier rebinning" (FORE)

The creation of the sinogram, including both the attenuation correction and the time of flight information and the geometric peculiarities of the respective scintillators, as well as the Fourier rebinning, can be considered as linear processes within the boundaries set by noise. The various corrections, however, can lead to deviations both from the expected Poisson statistics of the noise and from an inhomogeneous distribution of the noise relative to the field of view of the tomograph.

Apart from the mentioned effects on the properties of the noise component, it remains possible for this "primary" sinogram to define a non-stationary but linear system transfer function. On the basis of such a transfer function thus quantitative measurements are possible.

In a further step, numerical methods ("sinogram restoration methods") can be used to increase the resolution of the sinogram by inverse filtering. The application of a Wiener filter (Viennese deconvolution) may have a positive effect on the spatial resolution, but in return increases the noise component and leads to a further distortion of the statistical properties of the noise component [HERR06].

More advanced numerical methods applied to the sinogram, such as an iterative deconvolution ("maximum likelihood deconvolution") from a non-stationary transfer function, can further improve the resolution of the sinogram depending, inter alia, on the local noise component and the data itself. These methods can therefore have strong non-linear effects and should therefore be avoided in the context of quantitative measurements.

PET image reconstruction

Starting from the sinogram, the actual image or the data volume resulting from the measurement is calculated in the third step (reconstruction). Filtered back projection (FBP) is a simple, reliable, fast and above all linear method suitable for this purpose. In imaging, reconstruction by FBQ achieves acceptable spatial resolution relative to the full width half maximum (FWHM) of the resulting PSF, however, the PSF exhibits a relatively wide foot which causes image blur and hinders quantitative measurements the foot of the PSF propagates in volume data sets in all three dimensions and causes a corresponding overflow effect between voxels ("spill in", "spill out").

In the context of quantitative measurements, it should be emphasized that FBP is basically a linear operation and leads, from a suitable sinogram, to a stable and reproducible PSF.

Unless already done in the sinogram, a damping correction can also be linked to the FBP or applied to the resulting image.

Modern, iterative, reconstruction methods based on statistical criteria such as "maximum likelihood expectation maximum" (MLEM) or "ordered subset expectation maximum" (OSEM) have become the standard for the reconstruction of PET images. In principle, these methods first implement a method which conversely allows the calculation of a sinogram based on an image and the known properties of the respective tomograph. The method then iteratively changes an initially coarse image until the sinogram calculated for the respective image shows, according to statistical criteria, the best possible agreement with the sinogram generated from the actual measurement. By specifying suitable constraints, the process is controlled to provide a suitable compromise between increased spatial resolution, suppression of the foot of the transfer function, and the resulting image noise. However, due to the statistical nature of the iterative methods, they are sensitive to variations in the noise of the original measurement as well as to image information itself.

Therefore, while the iterative methods show a higher spatial resolution compared to the FBP and thus also the disturbing influence of the PVE quantitative measurements on relatively small objects, it remains unclear how far these improvements actually reach.
However, with overall improved imaging and measurement accuracy, but actually in each individual case of unknown and variable PSF, the utility of iterative methods in terms of the required comparability of measurements remains limited especially in the context of multi-centric studies.

The Standardized Uptake Value (SUV)

• "Der SUV ist eine gemessene Aktivitätskonzentration in Bq/ml innerhalb eines definierten Volumens ("Volume of interest") bezogen auf die injizierte Aktivität in Bq pro Körpergewicht des Patienten in g gemessen zu einem definierten Zeitpunkt nach der Injektion."

Diese Definition führt nicht auf einen dimensionslosen Wert sondern resultiert formal in einer Einheit g/ml.
Andere Varianten verwenden die Körperoberfläche des Patienten als Bezugsmaß für die Normierung [THIE04].
Die vorwiegend verwendete Formel für die Berechnung des SUV ausgehend von "activity concentration" innerhalb eines "volume of interest" (ACvoi), der injizierten Dosis (FDGdose) und dem Körpergewicht (BW) wird von Boellard [BOEL09] angegeben als: $$\mathit{SUV}=\frac{\mathit{ACvoi}\left[\mathit{kBq}/\mathit{ml}\right]}{\mathit{FDGdose}\left[\mathit{MBq}\right]/\mathit{BW}\left[\mathit{kg}\right]}$$

In the context of PET, the concept of the SUV describes the accumulation of radioactive markers in tissue depending on the total injected dose and the weight of the patient. The SUV is widely used as a measure and should provide comparable results. However, the concept since its introduction shows a remarkable development and variability. The early definitions describe measured activity per gram of tissue and weight of the patient in terms of injected activity [OLDE74] [WOOD75]. The original definition of SUV [STRA91] was defined as the concentration in tissue (mCi / g) per injected dose (mCi / g) per body weight of the patient (g). This results in a dimensionless absolute value which can be regarded as the ratio between the activity measured in a defined volume and an averaged activity in relation to the whole body. A more recent definition in the clinical context can be rewritten as follows:

• "The SUV is a measured activity concentration in Bq / ml within a defined volume (" volume of interest ") relative to the injected activity in Bq per body weight of the patient in g measured at a defined time after injection."

This definition does not lead to a dimensionless value but results formally in a unit g / ml.
Other variants use the patient's body surface as a reference for normalization [THIE04].
The predominantly used formula for calculating the SUV from activity concentration within a volume of interest (ACvoi), injected dose (FDGdose) and body weight (BW) is given by Boellard [BOEL09] as: $$\mathit{SUV}=\frac{\mathit{ACvoi}\left[\mathit{kBq}/\mathit{ml}\right]}{\mathit{FDGdose}\left[\mathit{MBq}\right]/\mathit{BW}\left[\mathit{kg}\right]}$$

Unfortunately, the definitions do not suggest a methodology for describing the "volume of interest" (VOI), which is a very different way of performing the actual measurement with correspondingly different results allowed [BOEL03]. The extremely critical influence of the definition of the volume of interest to be measured on the result of the measurement is well known [KEYE95].
Therefore, by far the most common method of SUV measurement is the determination of the SUV _max , ie it is used as a measure of the activity of the largest value that a single voxel within the VOI shows. The simple adoption of this maximum value avoids the need for a more precise definition of the actual VOI and thus avoids the influence of, for example, a manual definition of the VOI or a rewriting of the VOI by means of a threshold value [BOEL09]. This despite the obvious drawbacks associated with a single voxel-based measurement.

Measurement of SUV _max

The activity concentration is statistically defined as the mean number of radioactive decays per time and volume. The actual measurement of an activity concentration is therefore bound to a suitable definition of the respective measurement volume. Strictly speaking, it is therefore not possible to specify an activity concentration without simultaneously describing the corresponding measurement volume. Furthermore, the definition implies that the measurement of a poisson is subject to statistics, ie the measurement accuracy is limited in any case by photon noise ("shot noise") or correspondingly by the number of detected decays within the measurement volume during the measurement time.
The number of detected decays can be regarded as a proportion of the actual decays corresponding to the detection sensitivity and reduced according to the respective absorption.
In contrast to the simplifying models described in the literature, the definition of the activity concentration must therefore contain a description of the measurement process and thus directly refer to the parameters of the PET / CT system used in each case. With respect to the measurement using a single voxel, a definition must be something like this:

The measured activity concentration relative to a single voxel of a PET image data set represents the number of radioactive decays detected via a mean spatial weighted average of a region centered around the respective voxel and corrected for the detection sensitivity of the system and each of them attenuation dependent on the measurement situation. "

Thus, a measurement of the SUV _{max is} initially inseparably connected to the spatial transfer function (PSF) of the tomograph, which measures the measurement volume defined, and further at least with respect to the statistical accuracy of the measurement depending on the sensitivity of the scanner and the respective attenuation.

In the case of spatial variations of the activity concentration in the order of magnitude of the voxel size, the measurement result is additionally disturbed by the sampling process since the respective spatial maxima of an activity concentration do not coincide with the respective centers of the voxels themselves but have a random distribution relative to their position within the voxel grid.

Partial volume effect

The partial volume effect ("partial volume effect" or "spill in" and "spill out") is the most important factor limiting quantitative PET / CT measurements [SORE07]. The PVE is caused by the limited spatial resolution of the scanner and is usually described as dependent on the PSF's "Full Width Half Maximum" (FWHM). In practice, the PVE concerns all measurements on structures with diameters less than about 3 times the FWHM. Accordingly, measurements become generally unreliable when the activity distribution shows structures with spatial frequencies below about 3 times the FWHM.
The cause of the PVE is that, as described above, the measurement of activity concentration always represents a weighted average over a region described by the PSF. However, the spurs of the PSF go far beyond the FWHM. In 3-dimensional imaging, the effect is exacerbated by the fact that the extensions of the PSF in all three dimensions reach into the surrounding volume and therefore are weighted higher with the square of the distance to the center of the respective voxels. The diameter of the region, which contributes significantly to the signal is thus significantly larger than the FWHM of the PSF. This influence of the environment on each local measurement falsifies the measurement results in particular for measurements of the activity concentration on small structures. Furthermore, the influence of the environment on the respective measurement by the FWHM is not adequately described. Rather, a knowledge of the exact shape of the PSF and in particular the peripheral areas of the PSF is required. An accurate knowledge of the PSF allows, within certain limits, a correction of the PVE by deconvolution.
In particular, the PVE is in principle completely complete by the respective effective PSF of the measurement. Are defined.

Clinical PET protocols for quantitative measurements

PET recordings for a quantitative analysis require strict adherence to examination protocols, including preparation of patients, preparation and injection of the radioactive marker, the technical parameters of the recording itself, the procedures for the reconstruction of the images and, of course, the methods of numerical analysis of the data to determine the respective measured value. Furthermore, a calibration or an adjustment of the tomographs used is required.
Particularly in the context of multi-centric medical studies, the requirements for uniform examination protocols, the comparison of the tomographs and the methods for the determination of quantitative values are currently being discussed intensively [WAHL09], [BOEL09], [BOEL09b], [DELB06], [SHYA08], [SCHE09]. Although these proposals already contain extensive specifications for the required examination protocols, the measured values are nevertheless subject to great variations due to the different imaging properties of the PET / CT systems available in the respective institutions [WEST2006].
The problem is aggravated by the fact that the systems have a growing number of variable technical parameters which allow imaging optimization for certain applications, but at the same time hinder a quantitative evaluation of the manipulated images.
To improve this situation, the methods claimed herein aim to compensate for the differences in imaging characteristics of the respective imaging systems.

In the context of quantitative measurements, it is proposed to carry out two reconstructions for each PET image in the future and to handle the resulting image pairs in parallel. A first reconstruction is performed for optimal imaging using the iterative numerical methods to increase spatial resolution and contrast, according to clinical routine. For the quantitative measurements, a second reconstruction is carried out in parallel, which is limited to the largely linear methods. This second reconstruction - hereinafter referred to as linear reconstruction - is useful as a starting point for quantitative measurements using the methods claimed herein, since the restriction to linear reconstruction can ensure a stable transfer function of the system.

Cross calibration using Recovery Factors.

The absolute calibration of PET systems in terms of measuring an activity concentration is a challenging task [GEWO02].

Nevertheless, a mutual comparison of different PET systems with respect to large homogenous sources, such as a commercially available 68Ge doped cylinder phantom (20 cm diameter), is relatively easy to perform [SCHE09].
This is indeed possible because the diameter of the homogeneous phantom far exceeds the diameter of the PSF of PET systems.
For smaller objects, this type of alignment no longer works because the measurements are influenced by the PVE, which varies considerably depending on the FWHM of the PSF as well as the exact shape of the PSF. Since the PSFs of different tomographs differ significantly from each other and the PVE can not be corrected without additional information, a simple comparison of different PET systems is not possible.
A current approach to overcome this problem is the measurement of "recovery factors" using phantom measurements on spheres with homogeneous activity concentration but of different size.
For the respective tomograph, it is determined in each case what proportion (= "recovery factor") of the actual activity concentration in the center of the respective sphere is still measured. In other words, the PVE is determined for homogeneous spheres of known size in a homogeneous environment by a measurement.
In later measurements, assuming that the object to be measured is approximately spherical, then a homogeneous activity concentration in a homogeneous environment and the diameter can be determined elsewhere - for example in CT image, with the help of the appropriate recovery factor on the actual Activity concentration are closed [SHYA08]. Of course, this method is subject to the restriction that the results are accurate only for spherical, homogeneous objects, further to the restriction that the exact size of the sphere must be determined otherwise. Furthermore, possibly inaccuracies occur in different tomographs with different PSF in very different ways, which makes it very difficult to compare the results for different tomographs.

The methods claimed here are therefore primarily not aimed at an indeterminate absolute correction of the PVE but directly at a comparison of the measurement results of different tomographs.
Basis of the claimed method is therefore not the determination of recovery factors but -ggf. using a suitable phantom to determine the actual PSF of the different imaging systems.

Solid state phantom (Solid State Phantom)

Calibration measurements using a phantom or other radiation source are a basis of quality assurance for PET systems [DAUB02]. As a rule, corresponding recovery factors are determined using spheres of homogeneous activity concentration of different size, as described above. Although occasionally additional point source measurements are taken to measure the FWHM, the particular shape of the PSF is typically not measured or determined more accurately.

• Es handelt sich um ein Festkörperphantom, das leicht transportabel ist und dessen Kugeln nicht von Messung zu Messung neu befüllt werden müssen.
• Das Phantom enthält verglichen mit dem Standardphantom mehr, welche zusammen einen grösseren Bereich an Durchmessern abdecken.
• Und die Kugeln sind auch einzeln in ganz unterschiedlichen Anordnungen handhabbar, was eine schnelle Realisierung von an die jeweilige Anwendung angepassten speziellen Phantomen erlaubt, etwa eine Positionierung in der Nähe von Absorbern oder in Hohlräumen oder beides.

Die Verwendung eines Festkörperphantoms auf Basis des relativ langlebigen ⁶⁸Ge Isotops vermeidet das ansonsten erforderliche wiederholte Befüllen der Kugeln und vereinfacht die Handhabung der Kugeln deutlich. Damit wird eine ganze Reihe von Fehlermöglichkeiten vermieden und insbesondere auch die Strahlenbelastung der mit der Handhabung des Phantoms betrauten Personen deutlich vermindert.
Weiter ist gegenüber einem mit Aktivität in flüssiger Form zu befüllenden Phantom die Handhabung des Festkörperphantoms insgesamt deutlich einfacher und dies unabhängig von der Anzahl der Kugeln, die es enthält. Davon ausgehend und um eine genauere Bestimmung der PSF zu ermöglichen und unter Berücksichtigung der höheren räumlichen Auflösung moderner PET/CT Systeme wurde die Reihe der Kugeln hin zu kleineren Durchmessern erweitert.
Das für die Evaluation der beanspruchten Verfahren hergestellte Phantom verwendet 12 Hohlkugeln welche Volumen von 16ml bis herunter zu 1/128 ml umfassen entsprechend Durchmessern von rund 31 mm bis herunter zu 2,5 mm. Die Kugeln wurden homogen befüllt mit einem Epoxid-Harz versetzt mit einer Aktivitätskonzentration von 0,1 MBq/ml. Nach dem Aushärten des Harzes und zusätzlicher Versiegelung der Öffnungen zum Befüllen der Kugeln, können diese ohne Gefahr einer Kontamination in einfacher Weise gehandhabt werden.In order to determine the PSF, the use of a novel solid-state phantom is proposed here, differing from the otherwise obvious use of a point source. This phantom differs from the currently available standard active-sphere phantoms, for example, according to the NEMA / IEC 2001 standard in three main respects:

• It is a solid-state phantom that is easy to transport and whose balls do not have to be refilled from measurement to measurement.
• The phantom contains more compared to the standard phantom, which together cover a larger range of diameters.
• And the balls can also be handled individually in completely different arrangements, which allows a quick realization of special phantoms adapted to the respective application, for example a positioning close to absorbers or in cavities or both.

The use of a solid-state phantom based on the relatively durable ⁶⁸ Ge isotope avoids the otherwise required repeated filling of the balls and simplifies the handling of the balls clearly. This avoids a whole series of possible errors and in particular significantly reduces the radiation exposure of the persons entrusted with the handling of the phantom.
Furthermore, compared with a phantom to be filled with activity in liquid form, the handling of the solid-state phantom is considerably simpler overall, regardless of the number of spheres it contains. From this, and to allow a more accurate determination of the PSF, and taking into account the higher spatial resolution of modern PET / CT systems, the series of spheres has been extended to smaller diameters.
The phantom prepared for the evaluation of the claimed methods uses 12 hollow spheres ranging in volume from 16 ml down to 1/128 ml, corresponding to diameters from about 31 mm down to 2.5 mm. The spheres were filled homogeneously with an epoxy resin mixed with an activity concentration of 0.1 MBq / ml. After the curing of the resin and additional sealing of the openings for filling the balls, they can be handled in a simple manner without the risk of contamination.

The spheres were mounted within a Plexiglass cylinder of 22 cm diameter diameter on 2 concentric circles. On the outer circle with a diameter of about 14 cm, the 6 larger balls are mounted, on the inner circle with about 7 cm diameter, the 6 smaller balls. The Plexiglass cylinder can be filled with water.
Further, the individual balls are designed and provided with a suitable thread for attachment, that they can be used in a simple manner within other arrangements. In particular, it is possible in a simple manner to construct an arrangement in the context of specific medical questions which simulates certain anatomical conditions with regard to the radiological properties. In the context of, for example, medical studies using PET / CT recording, with such phantoms specially adapted to the problem, the accuracy of the comparison of different devices for precisely this question can be further increased.

Determination of the spatial transfer function (PSF)

The process of imaging is usually represented as the image (img) as the convolution (convolution) of an original image (obj) representing the object with a spatial spread function (PSF) specific to the imaging device. $$\mathit{obj}\otimes \mathit{psf}=\mathit{img}$$

Obviously, the PSF (psf) can therefore be defined as the image of a point source (point) in the center of the coordinate system. $$\mathit{point}\otimes \mathit{psf}=\mathit{psf}$$

Usually, the PSF of an imaging system or a tomograph is measured from equation (3) on the basis of the image of a point source, i. using a source whose diameter is much smaller than the FWHM of the PSF to be measured.

In fact, however, this method is not always optimal, since the mapping of a point source generally does not correspond to the actual application of the system. Typically, objects with finite-size structures are mapped, and it seems plausible to determine the PSF also from objects whose size is in the range of the sizes of the objects usually to be imaged or of interest.

For the determination of the PSF of a PET system, therefore, a measurement on the above-described phantom ie measurements on homogeneous spheres of known size is proposed starting directly from equation (2).

In the case of an exactly known object and thus of an exactly known original image (obj) and in the case of the present, measured image (img), the PSF can be calculated by numerical deconvolution ie by convolution of the image (img) with the inverse Fourier transform of the object (obj ^{). 1} ) are determined according to the following equation: $$\mathit{psf}=\mathit{img}\otimes {\mathit{obj}}^{-1}$$

In practice, numerical determination of the PSF by iterative numerical methods of deconvolution starting from Equation 2 is readily possible. This method is obviously more robust than the usual method using a point source, because a larger number of voxels contribute to the result, and because the baseline measurements on several differently sized spheres are close to the context of the actual clinical measurements sought.
Starting from a single measurement of the described phantom, it is therefore possible to obtain both the effective PSF and an absolute measure for the matching of different PET systems. Furthermore, a measure of the sensitivity results in the form of a determinable signal-to-noise ratio relative to measurement situations which can be represented by the phantom.
It should be noted that the PSF of a PET system is usually not stationary and subject to systematic broadening with increasing transaxial distance from the center of the field of view. Depending on the requirements, this spatial variation of the PSF must be taken into account accordingly. This can be done by means of several measurements of the phantom at different positions in the field of view of the tomograph and the calculation and representation of a location-dependent PSF by suitable interpolation or extrapolation of each determined at the different locations from the measurement local PSFs or by a mathematical transformation of the measured local PSF according to known technical characteristics of the respective scanner.

Transkonvolution

$$\mathit{obj}\otimes {\mathit{psf}}_2={\mathit{img}}_2$$

As shown above, the measurement of the SUV is inextricably linked to characteristics of the tomograph. In particular, the determination of the SUV _{max is} directly related to the PSF of the respective tomograph.
Strictly speaking, an absolute determination of the SUV is not only impossible, at least for small objects, but not even definable, since the measurement of an activity concentration always presupposes a certain measurement volume. As This measurement volume is defined by the PSF of the respective tomograph.
In order to obtain valid and comparable values for SUV measurements, it would therefore be necessary to standardize the PSF of the tomographs used, or in other words to use a standard tomograph for all measurements. Unfortunately, the competing manufacturers of PET / CT systems, for understandable reasons, have no interest in producing standardized tomographs with identical characteristics for all manufacturers.
To overcome this problem, a new numerical method is proposed, which is referred to below as transconvolution.
To explain the method, first two different imaging systems are defined as follows: $$\mathit{obj}\otimes {\mathit{psf}}_1={\mathit{img}}_1$$

$$\mathit{obj}\otimes {\mathit{psf}}_2={\mathit{img}}_2$$

The two different spatial transfer functions psf ₁ and psf ₂ represent the two different tomographs or different imaging systems which respectively generate the two different images img ₁ and img _{2 of} the same object obj .
Mathematically theoretically the object could be reconstructed by deconvolution, ie an inverse filtering of the following form: $${\mathit{img}}_1\otimes {\mathit{psf}}_1^{-1}=\mathit{obj}$$

For real measurements with limited number of sample points (sampling), limited resolution and in the presence of noise, such deconvolution is only possible to a very limited extent. In particular, the inverse of the transfer function ( psf ₁ ^{- 1} ) can not usually be represented numerically.
However, from equations (5) and (6) follows: $${\mathit{img}}_1\otimes {\mathit{psf}}_1^{-1}\otimes {\mathit{psf}}_2={\mathit{img}}_2$$

This formula illustrates how in known spatial transfer functions of the respective imaging systems (psf1, psf2) the image of an object as created by a first imaging system (img1) can be transformed to form a second image (img2 ) corresponding to the image of the object as it would have been created by a second different imaging system.

$${\mathit{img}}_1\otimes \mathit{tf}={\mathit{img}}_2$$

For further explanation, the transvolution function (tf) is introduced as follows: $$\mathit{tf}\equiv {\mathit{psf}}_1^{-1}\otimes {\mathit{psf}}_2$$

$${\mathit{img}}_1\otimes \mathit{tf}={\mathit{img}}_2$$

$$F\left({\mathit{img}}_1\right)\cdot F\left(\mathit{tf}\right)=F\left({\mathit{img}}_2\right)$$

In general, the inverse of a PSF can not be represented numerically so that ( psf ₁ ^{- 1} ) can not be fully defined. However, the convolutions described by equations (8) and (9) can be easily represented after Fourier camouflage in frequency space as follows: $$F\left(\mathit{tf}\right)\equiv F\left({\mathit{psf}}_1^{-1}\right)\cdot F\left({\mathit{psf}}_2\right)$$

$$F\left({\mathit{img}}_1\right)\cdot F\left(\mathit{tf}\right)=F\left({\mathit{img}}_2\right)$$

Starting from a spatial transfer function psf , the term | F ( psf ) | defined as the corresponding Modulation Transfer Function (MTF) of the system relative to the transmitted spatial frequencies. For any realistic imaging system, the MTF will drop to higher spatial frequencies and eventually fall above a certain cutoff frequency below any existing noise level. Obviously, the inverse of a spatial transfer function can only be meaningfully determined for values below this cutoff frequency. This fact is the deeper reason for the principal limits of deconvolution.
The mathematical and metrological background was worked out in detail eg in the context of inverse filtering, in particular the Wiener filter.
In the field of numerical image processing, the method of convolution using the Fourier transform is often used for the filtering of images. Such a filter represents a spatial transfer function (psf) in the frequency domain through a "window function" which actually represents a corresponding MTF. It is important that as window functions it makes sense to use apodization functions which drop to 0 above a certain cutoff frequency.
One of the frequently used window functions is the Hanning function H ("raised cosine window"), which, as a filter, causes smoothing by completely suppressing spatial frequencies above a certain cutoff frequency but at the same time produces relatively low artifacts such as overshoots due to its uniform shape in the filtered image caused by edges.

$$H_{\omega }\left(\nu \right)\equiv 0f\ddot{\mathrm{u}}r\left|\nu \right|>\pi$$

A Hanning function with variable width and a freely definable limit frequency ω can be defined as follows: $$H_{\omega }\left(\nu \right)\equiv 0.5+0.5\cdot \cos \left(\mathit{\pi \nu }/\omega \right)f\ddot{\mathrm{u}}r\left|\nu \right|\le \pi$$

$$H_{\omega }\left(\nu \right)\equiv 0f\ddot{\mathrm{u}}r\left|\nu \right|>\pi$$

$$F\left({\mathit{ntf}}_{\omega }\right)\equiv F\left({\mathit{psf}}^{-1}\right)\cdot H_{\omega }$$

$$\mathit{img}\otimes {\mathit{psf}}^{-1}\otimes F^{-1}\left(H_{\omega }\right)={\mathit{img}}_n$$

Such a Hanning function or a comparable apodization function is suitable for use as MTF of a virtual imaging system. Accordingly, as an example using a Hanning function H _ω, a normalized transvolution can be defined as follows: $$F\left(\mathit{img}\right)\cdot F\left({\mathit{psf}}^{-1}\right)\cdot H_{\omega }=F\left({\mathit{img}}_n\right)$$

$$F\left({\mathit{ntf}}_{\omega }\right)\equiv F\left({\mathit{psf}}^{-1}\right)\cdot H_{\omega }$$

$$\mathit{img}\otimes {\mathit{psf}}^{-1}\otimes F^{-1}\left(H_{\omega }\right)={\mathit{img}}_n$$

Here, img is the image which was taken by the respective imaging system with the spatial Trannsfer function psf . The function ntf _ω is the normalized transconvolution function determined for the respective system based on the respective spatial transfer function, and img _n is the resulting normalized image as it would have been taken by a standardized virtual tomograph. Insofar as the parameter ω is not chosen to be too large, that is to say within the limits set by the spatial cut-off frequencies of the participating imaging systems, a numerical calculation is possible in any case.

Interpolation of non-stationary spatial transfer functions

In the case of tomographs or other complex imaging systems, the spatial transfer function is not stationary, ie location-dependent. The calculation of the convolutions becomes more complicated as a result, but can be carried out numerically according to the specified methods. If appropriate, the methods are to be adapted to the spatially varying spatial transfer functions by suitable interpolation or, if appropriate, piecewise calculation.

Application of the virtual tomograph in multi-centric PET studies

• An den beteiligten PET Systemen werden - nicht notwendigerweise zu Beginn der Studie - unter den Bedingungen des Untersuchungsprotokolls Phantom Messungen durchgeführt.

Diese Messungen werden in der beschriebenen Weise jeweils linear rekonstruiert und die jeweilgen PSF der beteiligten PET-Systeme bestimmt.
Wenn die verschiedenen PSF der beteiligten Systeme vorliegen kann eine geeignete räumliche Grenzfrequenz ω bestimmt werden und eine entsprechende standardisierte PSF für den virtuellen Tomographen gewählt werden, etwa in Form der in Gleichung (15) beschriebenen Funktion F ^-1(H _ω) .
In der Folge kann für jedes der beteiligten PET-Systeme die oben beschriebene Transkonvolution-Funktion ntf _ω bestimmt werden.Once a suitable protocol has been established, the virtual tomograph can be used in the context of quantitative studies as follows:

• Phantom measurements are performed on the participating PET systems, not necessarily at the beginning of the study, under the conditions of the study protocol.

These measurements are respectively linearly reconstructed in the manner described and the respective PSF of the PET systems involved is determined.
If the various PSFs of the systems involved are present, a suitable spatial cutoff frequency ω can be determined and a corresponding standardized PSF can be selected for the virtual tomograph, for example in the form of the function F ^-1 ( H _ω ) described in equation (15).
As a result, the above-described transconvolution function ntf _ω can be determined for each of the involved PET systems.

In the course of the multicenter study, in addition to the usual iterative reconstruction of an image data set for optimized imaging, a second linear reconstruction is calculated for each measurement and subjected to a convolution with the transconvolution function determined for the respective tomograph. The resulting quantitatively normalized second image data set represents the measurement as it would have been done by the virtual tomograph.
Both image data sets can be handled, visualized, evaluated and stored in parallel within the scope of the usual methods.
The visual assessment is based on the iteratively reconstructed and optimized for imaging image data sets, quantitative evaluations of whatever kind take place on the basis of said normalized image data sets. The results of these quantitative analyzes are then comparable for measurements of different systems.

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Claims (10)

1. A method for standardized and comparable determination of normalized quantitative measurement values based on images or image data acquired by different imaging systems,
   characterized by the following method steps:

   a) for each of said imaging systems a determination of acquisition parameters to be used to acquire said images or image data such that within the capabilities of said systems a most linear image acquisition is performed;

   b) for each of said imaging systems using said acquisition parameters a measurement or other determination of a stationary or non-stationary spatial transfer function (tf), which describes the imaging properties of the respective system;

   c) definition of a stationary or non-stationary spatial transfer function (ntf), which describes the imaging properties of a virtual normalized imaging system;

   d) numerical calculation of normalized images or image data ( n ) starting from images or image data ( d ) acquired by said imaging systems comprising Transconvolution, where said Transconvolution is representable as a convolution of the respective acquired images or image data ( d ) with the result of a convolution of the inverse of said spatial transfer function of the respective imaging system ( tf^-1 ) with said defined stationary or non-stationary spatial transfer function ( ntf ) of the virtual normalized imaging system: $$d\otimes {\mathit{tf}}^{-1}\otimes \mathit{ntf}=n;$$

   

   
   and

   e) determination of said normalized quantitative measurement values using said calculated normalized images or image data which correspond to said acquired images or image data.
2. A method according to claim 1 characterized in that
   the image data are two-dimensional and represent a measurement in two spatial dimensions, or that
   the image data are three-dimensional and represent a measurement in three spatial dimensions.
3. A method according to claim 1, characterized in that
   the image data in addition to either two or three spatial dimensions comprise one or more additional non-spatial dimensions and said method is carried out only with respect to the spatial dimensions.
4. A method according to one or more of claims 1 to 3, characterized in that said imaging systems are tomographic systems and said image data sets are sinograms.
5. A method according to one of claims 1 to 3, characterized in that said imaging systems are tomographic systems and said image data sets are reconstructed images.
6. A method according to one of claims 4 or 5, characterized in that said tomographic systems are emission tomographic systems and are able to perform attenuation correction.
7. A method according to claim 6, characterized in that said emission tomographic systems are PET / CT or SPECT / CT systems.
8. A method according to one of the preceding claims characterized in that said measurement of a stationary or non-stationary spatial transfer function ( tf ), which describes the imaging properties of the respective system, involves the use of a phantom.
9. A method according to claim 8, characterized in that said phantom contains solid state radiation sources of defined size, shape and activity, and can be used repeatedly for said measurement of a stationary or non-stationary spatial transfer function.
10. A method according to claim 9, characterized in that the determination of a stationary or non-stationary spatial transfer function ( tf ), which describes the imaging properties of the respective system, comprises a numerical interpolation or extrapolation of the non-stationary transfer function in accordance with known properties of the respective tomographic system in addition to said measurement using said phantom.